{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2b29ae44-3f5b-4df2-961c-631320eecf0c",
   "metadata": {},
   "source": [
    "# Example Community Notebook\n",
    "\n",
    "* Contributors: saitcakmak\n",
    "* Last updated: Jan 12, 2024\n",
    "* BoTorch version: 0.9.6(dev), commit hash: dccda59d8ef51d8074de82fdb5614bad2db0ee96\n",
    "\n",
    "In this notebook, we utilize the example GP model with randomly generated data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e45e2cb4-5ea1-4d72-8be7-806cacf80d01",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/saitcakmak/botorch/botorch/models/utils/assorted.py:202: InputDataWarning: Input data is not standardized (mean = tensor([0.1225]), std = tensor([0.7601])). Please consider scaling the input to zero mean and unit variance.\n",
      "  warnings.warn(msg, InputDataWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "from botorch_community.models.example import ExampleModel\n",
    "from gpytorch import ExactMarginalLogLikelihood\n",
    "from botorch.fit import fit_gpytorch_mll\n",
    "\n",
    "torch.set_default_dtype(torch.float64)\n",
    "X = torch.rand(10, 1)\n",
    "Y = torch.sin(X*5)\n",
    "\n",
    "model = ExampleModel(train_X=X, train_Y=Y)\n",
    "mll = ExactMarginalLogLikelihood(model.likelihood, model)\n",
    "fit_gpytorch_mll(mll)\n",
    "\n",
    "test_X = torch.linspace(0, 1, 100)\n",
    "with torch.no_grad():\n",
    "    posterior = model.posterior(test_X.view(-1, 1))\n",
    "mean, std = posterior.mean.squeeze(), posterior.variance.sqrt().squeeze()\n",
    "\n",
    "fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(8, 6))\n",
    "ax.set_title(\"Example Model Predictions\")\n",
    "ax.scatter(X, Y, c=\"b\", label=\"observations\")\n",
    "ax.plot(test_X, mean, label=\"predictions\")\n",
    "ax.fill_between(test_X, mean-2*std, mean+2*std, alpha=0.2)\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.17"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
